martingale

Definition

A process $(M_t)_{t \geq 0}$ is a martingale with regard to the filtration $(\mathscr{F}_t)_{t \geq 0}$ if for all $t \geq 0$, $M_t$ is $\mathscr{F}_t$-measurable and integrable, and

(conditional expectation)

See also

• stochastic process
• Markov process
• multiplicative martingale (Mandelbrot)

References

1. https://www.cs.yale.edu/homes/aspnes/pinewiki/Martingales.html
2. https://chewisinho.github.io/main.pdf, p. 5
3. https://math.mit.edu/~sheffield/2019600/martingalenotes.pdf